Unconditional bases and strictly convex dual renormings

TL;DR

This paper characterizes when Banach spaces with unconditional bases can be renormed so that their dual spaces become strictly convex, providing a comprehensive set of equivalent conditions.

Contribution

It offers new equivalent conditions for Banach spaces with unconditional bases to admit strictly convex dual norms, advancing the understanding of renorming theory.

Findings

Provides a set of equivalent conditions for such renormings

Establishes connections between unconditional bases and dual convexity

Enhances the theoretical framework for Banach space renormings

Abstract

We present equivalent conditions for a space $X$ with an unconditional basis to admit an equivalent norm with a strictly convex dual norm.